On this note are the following indorsements. Sept. 1, 1845, received two hundred and fifty dollars. Nov. 1, 1846, received two hundred dollars. What was due June 1, 1847 ? Ans. $242.75. OPERATION. $600 ×.10563.00, interest from June 1, 1844, to Sept. 1, 250 [1845. 350 x.07 24.50, interest from Sept. 1, 1845, to Nov. 1, 200 [1846. 150 x .035 92.75 $242.75 remains due June 1, 1847. 5.25, interest from Nov. 1, 1846, to June 1, $92.75, amount of interest. [1847. The above is the method of computing annual interest, when the contract is for a specified time. NOTE. The above methods of computing annual interest are not only practised in the courts of Vermont, but a similar method has been adopted in some of the courts of New Hampshire; but it is not the method in Massachusetts. SECTION XXXIX. MISCELLANEOUS PROBLEMS IN INTEREST. PRINCIPAL, interest, and time given, to find the rate per cent. 1. At what rate per cent. must $500 be put on interest to gain $120 in 4 years? OPERATION. $500 .01 5.00 4 BY ANALYSIS. The interest of $1 for the given time at one per cent. is 4 cents. $500 will be 500 times as much, $500.04 $20.00. = 20.00)120.00(6 per cent. Ans. Then, if $20 give 1 per cent. $120 will give 20,6 per cent. 120.00 RULE. Divide the given interest by the interest of the given sum at 1 per cent. for the given time, and the quotient will be the rate per cent. required. 2. At what rate per cent. must $120 be on interest, to amount to $133.20 in 16 months? Ans. 81 per cent. 3. At what rate per cent. must $280 be on interest to amount to $411.95 in 6 years? Ans. 74 per cent. Principal, interest, and rate per cent. given, to find the time. 4. How long must $500 be on interest at 6 per cent. to gain $120 ? $ 500 .06 OPERATION. BY ANALYSIS. We find the interest of $1.00 at the given rate for one year is 6 30.00)120.00(4 years, Ans. cents. $500 will, therefore, be 500 120.00 times as much,= $500 x .06 = $30.00. Now, if it take 1 year to gain $ 30, it will require 120 to gain $120,= 4 years, Ans. RULE. ·Divide the given interest by the interest of the principal for 1 year, and the quotient is the time. per cent. to Ans. 16 months. 5. How long must $120 be on interest at 8 amount to $133.20? 6. How long must $280 be on interest at 7 amount to $411.95 ? 1 per cent. to Ans. 6 years. Interest, time, and rate per cent. given, to find the principal. 7. What principal at 6 per cent. is sufficient in 4 years to gain $120? OPERATION. $1 .06 .06 4 .24)120.00($500, Ans. 120.00 RULE. Divide the given interest or amount by the interest or amount of $1 for the given rate and time, and the quotient is the principal. 8. What principal at 84 per cent. is sufficient in 16 months to gain $13.20 ? Ans. $120.00. 9. What principal at 7 per cent. is sufficient in 6 years to amount to $411.95? Ans. $280.00. SECTION XL. COMPOUND INTEREST. THE law specifies that the borrower of money shall pay a certain number of dollars, called per cent., for the use of one hundred dollars for a year. Now, if this borrower does not pay to the lender this per cent. at the end of the year, it is no more than just that he should pay interest for the use of it, so long as he shall keep it in his possession; and this is called Compound Interest. 1. What is the compound interest of $300 for 3 years? First Method. 1.06 18.00, interest for 1 year. 300 318.00, amount for 1 year. 1.06 19.08, int. for second year. 337.08, amount for 2 years. 20.22,48, int. for third year. 337.08 357.30,48, amount for 3 years. 300 $57.30,48, compound int. for 3yrs. Ans. $57.30,4. RULE. Find the interest of the given sum for one year, and add it to the principal; then find the interest of this amount for the next year; and so continue until the time of settlement. Subtract the principal from the last amount, and the remainder is the compound in terest 2. What is the amount of $500 for 3 years? Ans. $595.50,8. 3. What is the compound interest of $ 345 for 10 years? Ans. $272.84,2. 4. What is the compound interest of $316 for 3 years 4 months and 18 days? Ans. $69.01,7. By the aid of the following Table, calculations are more easily effected than by the preceding rule. TABLE, Showing the amount of 1 dollar, or 1 pound, for any number of years under 40, at 3, 4, 5, 6, and 7 per cent., compound interest. Years. 3 per cent. 4 per cent. 5 per cent. 1.030000 1.040000 1.050000 10 6 per cent. 7 per cent. Years. 1.070000 1 123456789 2.952164 16 3.158815 17 3.379932 18 3.616528 19 3 1.092727 1.124864 1.157625 1.191016 1.225043 4 1.125508 1.169858 1.215506 1.262476 1.310795 5 1.159274 1.216652 1.276281 1.338225 1.402552 6 1.194052 1.265319 1.340095 1.418519 1.500730 7 1.229873 1.315931 1.407100 1.503630 1.605781 8 1.266770 1.368569 1.477455 1.593848 1.718186 9 1.304773 1.423311 1.551328 1.689478 1.838459 1.343916 1.480284 1.628894 1.790847 1.967151 10 11 1.384233 1.539454 1.710339 1.898298 2.104852 11 12 1.425760 1.601032 1.795856 2.012196 2.252191 12 13 1.468533 1.665073 1.885649 2.132928 2.409845 13 14 1.512589 1.731676 1.979931 2.260903 2.578534 14 15 1.557967 1.800943 2.078928 2.396558 2.759032 15 16 1.604706 1.872981 2.182874 2.540351 17 1.652847 1.947900 2.292018 2.692772 18 1.702433 2.025816 2.406619 2.854339 19 1.753506 2.106849 2.526950 3.025599 20 1.806111 2.191123 2.653297 3.207135 3.869685 20 21 1.860294 2.278768 2.785962 3.399563 4.140563 21 22 1.916103 2.369918 2,925260 3.603537 4.430403 22 23 1.973586 2.464715 3.071523 3.819749 4.740530 23 24 2.032794 2.563304 3.225099 4.048934 5.072367 24 2.093777 2.665836|3.386354 4.291870 5.427434 25 26 2.156591 2.772469 3.555672 4.549382 5.807352 26 27 2.221289 2.883368 3.733456| 4.822345 6.213868 27 28 2.287927 2.998703 3.920129 5.111686 6.648838 28 29 2.356565 3.118651 4.116135 5.418387 7.114257 29 30 2.427262 3.243397 4.321942 5.743491 7.612255 30 31 2.500080 3.373133 4.538039 6.088100 8.145112. 31 32 2.575082 3.508058 4.764941 6.453386 8.715270 32 33 2.652335 3.648381 5.003188 34 2.731905 3.794316 5.253347 25 6.840589 9.325339 33 7.251025 9.978113 34 7.686086 10.676581 35 8:147252 11.423942 36 8.636087 12.223618 37 9.154252 13.079271 38 9.703507 13.994820 35 2.813862 3.946088 5.516015 39 To perform questions by the Table, multiply the amount of one dollar for the given rate and time found in the Table by the principal, and from the product subtract the principal, and the remainder is the compound interest. NOTE. If there be months and days, find the amount for them on the number taken from the Table, before it is multiplied by the principal. EXAMPLES. 5. What is the compound interest of $360 for 5 years, months, and 24 days? Ans. $138.14. OPERATION. 1.338225, amount of 1 dollar for 5 years. 5352900 6 4014675 .045499650 1.338225 1.383724650, amount of 1 dollar for 5yrs. 6mo. 24 days. 83023479000 415117395 498.14,0874000, amount of principal for 5yrs. 6mo. 24 days. 360 $138.14, compound interest of the principal for do. 6. What is the interest of $ 890 for 30 years? Ans. $4221.70,6. 7. What is the amount of $480 for 40 years? Ans. $4937.14,4. 8. What is the interest of $300 for 10 years, 7 months, and 15 days? Ans. $257.40,1. 9. What is the amount of $ 586 for 12 years, 1 month, and 29 days, at 5 per cent. ? Ans. $1060.99,5. 10. The probable number of blacks at this time (1835) in the United States is 2,500,000. Now, supposing their increase to be 25 per cent. for every 10 years, what will be their number in the year 1935 ? Ans. 23,283,057. 11. Supposing the annual increase of the people of color to be 2 per cent., how many must be sent out of the country each year, that their numbers might not increase? Ans. 50,000, 12. What is the amount of $900 for 7 years, at 5 per Ans. $1266.39. cent. ? |